The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A134163 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A134163

1 + 12*n + 81*n^3 + n*(105*n + 81*n^3)/2.
(history; published version)

#19 by Charles R Greathouse IV at Thu Sep 08 08:45:32 EDT 2022

PROG

(MAGMAMagma) [1 + 12*n + 81*n^3 + n*(105*n+ 81*n^3)/2: n in [0..30]]; // Vincenzo Librandi, May 09 2011

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#18 by Charles R Greathouse IV at Sat Jun 13 00:52:32 EDT 2015

LINKS

<a href="/index/Rec#order_05">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

Discussion

Sat Jun 13

00:52

OEIS Server: https://oeis.org/edit/global/2439

#17 by Michel Marcus at Fri Oct 24 06:09:55 EDT 2014

STATUS

reviewed

approved

#16 by Joerg Arndt at Fri Oct 24 06:02:31 EDT 2014

STATUS

proposed

reviewed

#15 by Michel Marcus at Fri Oct 24 02:33:18 EDT 2014

STATUS

editing

proposed

#14 by Michel Marcus at Fri Oct 24 02:33:09 EDT 2014

NAME

1 + 12n 12*n + 81n81*n^3 + n*(105n 105*n + 81n81*n^3)/2.

STATUS

proposed

editing

#13 by Wesley Ivan Hurt at Thu Oct 23 21:32:40 EDT 2014

STATUS

editing

proposed

#12 by Wesley Ivan Hurt at Thu Oct 23 21:32:09 EDT 2014

FORMULA

a(n) = ( sum_{k=1..3n+1} k^7 ) / ( sum_{k=1..2n3n+1} k^3 ).

#11 by Wesley Ivan Hurt at Thu Oct 23 21:30:42 EDT 2014

NAME

a(n) = 1 + 12n + 81n^3 + n(105n + 81n^3)/2.

COMMENTS

A000541(n) is divisible by A000537(n) if and only n is congruent to 1 mod 3 (see A016777).

LINKS

<a href="/index/ReaRec#recLCCorder_05">Index to sequences with linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

FORMULA

a(n) = (3(3n + 1)^4 + 6(3n + 1)^3 - (3n + 1)^2 - 4 (3n + 1) + 2)/6.

a(n) = Sum[( sum_{k=1..3n+1} k^7] ) /Sum[k^3], ( sum_{k, =1, 3n ..2n+ 1} k^3 ).

G.f.: -(1+182*x+606*x^2+182*x^3+x^4)/(-1+-x)^5. - R. J. Mathar, Nov 14 2007

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, Oct 23 2014

MAPLE

A134163:=n->1 + 12*n + 81*n^3 + n*(105*n + 81*n^3)/2: seq(A134163(n), n=0..30); # Wesley Ivan Hurt, Oct 23 2014

PROG

(MAGMA) [1 + 12*n + 81*n^3 + n*(105*n+ 81*n^3)/2: n in [0..30]]; // _Vincenzo Librandi, _, May 09 2011

KEYWORD

nonn,easy

STATUS

approved

editing

#10 by Russ Cox at Sat Mar 31 10:22:05 EDT 2012

AUTHOR

_Artur Jasinski (grafix(AT)csl.pl), _, Oct 10 2007

Discussion

Sat Mar 31

10:22

OEIS Server: https://oeis.org/edit/global/339